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Lie Algebraic Theory of Transfer Matrices in Ion Optics of Mass Spectrometers
Author(s) -
Erdélyi Béla
Publication year - 1996
Publication title -
rapid communications in mass spectrometry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.528
H-Index - 136
eISSN - 1097-0231
pISSN - 0951-4198
DOI - 10.1002/(sici)1097-0231(19960715)10:9<1001::aid-rcm567>3.0.co;2-8
Subject(s) - computation , algebraic number , chemistry , spectrometer , theoretical physics , algebra over a field , optics , physics , algorithm , computer science , pure mathematics , mathematical analysis , mathematics
A new classical perturbative method, based on Lie algebraic technics, is presented for ion optical calculations and construction of transfer matrices for autonomous systems, that is mass spectrometers based on electromagnetic fields which are independent of the distance along the optic axis and neglecting the influence of fringe fields. Some hints are given for the general case also. The method is presented in an algorithmic fashion, including the treatment of system parameters and errors, and several examples of standard optical modules are given. The relations among aberration coefficients and in principle the transfer matrices that can be derived using the theory are unlimited in order. It is hoped that the method will facilitate computations of transfer matrices and provide insight and improved design as a consequence of the Lie algebraic tools, as an optimal method to describe charged particle optical systems.